Objective Bayesian Upper Limits for Poisson Processes
Luc Demortier · 2005
We discuss the Bayesian approach to the problem of extracting upper limits on the rate of a Poisson process in the presence of uncertainties on acceptance and background parameters. In single-channel searches, we show that the usual choice of prior leads to a divergent posterior density from which no upper limit can be extracted. We propose a solution to this problem, that involves making more e‐cient use of the information contained in the data. We then generalize this solution to multiple-channel searches, and describe an importance sampling Monte Carlo method to perform the corresponding multi-dimensional integration. The frequentist properties of the proposed method are also studied.